Right now, there is no way to add buttons via the Platform Apps. We intentionally limit the locations in the UI that can be altered, to make the upgrade path easier between versions of SW. However, it's possible that in the future we could add specific locations where buttons can be added (like the New Ticket form).
Yes, if your App uses a Ticket placement, it will have access to the current ticket and if your App uses a Device placement, it will have access to the current device. The 'showTicket' event will fire when the placement is loaded, containing the id of the current ticket: developers.spiceworks.com/documentation/cloud-apps/reference/helpdesk/#show-ticket. If you need the full ticket object, you can then query for that id with the ticket API developers.spiceworks.com/documentation/cloud-apps/reference/helpdesk#get-a-single-ticket. The same can be done for the current device using the 'showDevice' event and the device API: developers.spiceworks.com//documentation/cloud-apps/reference/inventory/.